Developing further connections with Allied city-states, enlightened rulers send them some of their own bright scholars, who engage in scientific discussions with the local community. The resulting debate and exchange of ideas brings new scientific understanding which may greatly help the empire's technological development!

The power of Scholasticism increases the more Allied city-states you have, and the more technologically developed they are. Note that Friendly City-States won't contribute, just Allies! Of course, there's no way to tell in-game how much Science a particular City-State produces, but it stands to reason that those with a larger Population produce more Science.

So, if you're strong in Diplomacy and manage to have more than 1-2 Allies at any time, you may consider adopting this Policy even if you don't intend developing the full Patronage tree. It's a level 2 Policy, which means you only need Philanthropy to unlock it. And if you intend to finish this tree, you will need Scholasticism to progress further anyway. The only consideration then may be how many Allies you have at the moment, and whether Consulates will yield a more immediate benefit (if you don't have it yet).

Scholasticism is a style of teaching employed in medieval European universities from around 1000-1500 AD. The method emphasized critical reasoning and debate. The teacher would choose a book for study, and then he and the students would debate the meaning of the book, examine other books on the same topic, examine any criticism of the work, and so forth, by so doing gaining a fuller understanding of the topic than might be gained by rote memorization. The movement was largely fueled by the rediscovery of the works of Greek philosophers and subsequent attempts to integrate them with Christianity.